In mathematics, a radially unbounded function is a function for which Or equivalently, Such functions are applied in control theory and required in optimization for determination of compact spaces. Notice that the norm used in the definition can be any norm defined on , and that the behavior of the function along the axes does not necessarily reveal that it is radially unbounded or not; i.e. to be radially unbounded the condition must be verified along any path that results in: For example, the functions are not radially unbounded since along the line , the condition is not verified even though the second function is globally positive definite. References Real analysis Types of functions